论文标题
在集群倾斜的代数上
On the radical of Cluster tilted algebras
论文作者
论文摘要
我们确定了最小的下限$ n $，其中$ n \ geq 1 $，其中$ n $ th $ th $ n $ th $ n $ the the代表类别的激进分子倾斜代数消失。我们就下划线颤抖的顶点的数量给出了这样的约束。因此，我们获得了表示代表限制的自注射集群倾斜代数的模块类别的基础索引。我们还研究了$ m $，$ m \ ge 2 $的非零成分，在表示$（m+1）$的代表群集倾斜的代数中，不可兼容的模块之间的不可约合的形态，其模块类别的根本性。
We determine the minimal lower bound $n$, with $n \geq 1$, where the $n$-th power of the radical of the module category of a representation-finite cluster tilted algebra vanishes. We give such a bound in terms of the number of vertices of the underline quiver. Consequently, we get the nilpotency index of the radical of the module category for representation-finite self-injective cluster tilted algebras. We also study the non-zero composition of $m$, $m \ge 2$, irreducible morphisms between indecomposable modules in representation-finite cluster tilted algebras lying in the $(m+1)$-th power of the radical of their module category.
